\(\int \frac {\sqrt {\arccos (a x)}}{x} \, dx\) [79]

Optimal result

Integrand size = 12, antiderivative size = 12 \[ \int \frac {\sqrt {\arccos (a x)}}{x} \, dx=\text {Int}\left (\frac {\sqrt {\arccos (a x)}}{x},x\right ) \]

[Out]

Unintegrable(arccos(a*x)^(1/2)/x,x)

Rubi [N/A]

Not integrable

Time = 0.01 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00, number of steps used = 0, number of rules used = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \frac {\sqrt {\arccos (a x)}}{x} \, dx=\int \frac {\sqrt {\arccos (a x)}}{x} \, dx \]

[In]

Int[Sqrt[ArcCos[a*x]]/x,x]

[Out]

Defer[Int][Sqrt[ArcCos[a*x]]/x, x]

Rubi steps \begin{align*} \text {integral}& = \int \frac {\sqrt {\arccos (a x)}}{x} \, dx \\ \end{align*}

Mathematica [N/A]

Not integrable

Time = 0.20 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.17 \[ \int \frac {\sqrt {\arccos (a x)}}{x} \, dx=\int \frac {\sqrt {\arccos (a x)}}{x} \, dx \]

[In]

Integrate[Sqrt[ArcCos[a*x]]/x,x]

[Out]

Integrate[Sqrt[ArcCos[a*x]]/x, x]

Maple [N/A] (verified)

Not integrable

Time = 1.05 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.83

\[\int \frac {\sqrt {\arccos \left (a x \right )}}{x}d x\]

[In]

int(arccos(a*x)^(1/2)/x,x)

[Out]

int(arccos(a*x)^(1/2)/x,x)

Fricas [F(-2)]

Exception generated. \[ \int \frac {\sqrt {\arccos (a x)}}{x} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate(arccos(a*x)^(1/2)/x,x, algorithm="fricas")

[Out]

Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (co
nstant residues)

Sympy [N/A]

Not integrable

Time = 0.40 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.83 \[ \int \frac {\sqrt {\arccos (a x)}}{x} \, dx=\int \frac {\sqrt {\operatorname {acos}{\left (a x \right )}}}{x}\, dx \]

[In]

integrate(acos(a*x)**(1/2)/x,x)

[Out]

Integral(sqrt(acos(a*x))/x, x)

Maxima [F(-2)]

Exception generated. \[ \int \frac {\sqrt {\arccos (a x)}}{x} \, dx=\text {Exception raised: RuntimeError} \]

[In]

integrate(arccos(a*x)^(1/2)/x,x, algorithm="maxima")

[Out]

Exception raised: RuntimeError >> ECL says: expt: undefined: 0 to a negative exponent.

Giac [N/A]

Not integrable

Time = 0.45 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00 \[ \int \frac {\sqrt {\arccos (a x)}}{x} \, dx=\int { \frac {\sqrt {\arccos \left (a x\right )}}{x} \,d x } \]

[In]

integrate(arccos(a*x)^(1/2)/x,x, algorithm="giac")

[Out]

integrate(sqrt(arccos(a*x))/x, x)

Mupad [N/A]

Not integrable

Time = 0.25 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00 \[ \int \frac {\sqrt {\arccos (a x)}}{x} \, dx=\int \frac {\sqrt {\mathrm {acos}\left (a\,x\right )}}{x} \,d x \]

[In]

int(acos(a*x)^(1/2)/x,x)

[Out]

int(acos(a*x)^(1/2)/x, x)